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The Virtual Poincaré Polynomials of Homogeneous Spaces
Published online by Cambridge University Press: 04 December 2007
Abstract
We factor the virtual Poincaré polynomial of every homogeneous space G/H, where G is a complex connected linear algebraic group and H is an algebraic subgroup, as $t^{2u} (t^2-1)^r Q_{G/H}(t^2)$ for a polynomial $Q_{G/H}$ with nonnegative integer coefficients. Moreover, we show that $Q_{G/H}(t^2)$ divides the virtual Poincaré polynomial of every regular embedding of G/H, if H is connected.
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- © 2002 Kluwer Academic Publishers
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